This paper elucidates the conceptual role that independent randomization plays in non-cooperative game theory. In the context of large (atomless) games in normal form, we present precise formalizations of the notions of a mixed strategy equilibrium (MSE), and of a randomized strategy equilibrium...

We show that a rational expectations equilibrium need not be incentive compatible, need not be implementable as a perfect Bayesian equilibrium and may not be fully Pareto optimal, unless the utility functions are state independent. A comparison of rational expectations equilibria with core...